Acta Applicandae Mathematicae

, Volume 96, Issue 1, pp 55–69

Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes

Article

DOI: 10.1007/s10440-007-9095-0

Cite this article as:
Belopolskaya, Y. & Woyczynski, W.A. Acta Appl Math (2007) 96: 55. doi:10.1007/s10440-007-9095-0

Abstract

We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE.

Keywords

Stochastic flowsDiffusion processNonlinear parabolic equationsCauchy problem

Mathematics Subject Classification (2000)

60H1060J6035G0535K45

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsSt. Petersburg State University for Architecture and Civil EngineeringSt. PetersburgRussia
  2. 2.Department of Statistics, and Center for Stochastic and Chaotic Process in Science and TechnologyCase Western Reserve UniversityClevelandUSA